ibworking Posted February 15, 2010 Report Share Posted February 15, 2010 I have been assigned stellar numbers portfolio for this year, which is due in two-three weeks. I have been working on it for a while, and I have figure most of it out. The only thing I'm stumped on is the star numbers formula relating to terms of n. I have got the formula which works but I have no idea what to do to get the formula. Any help given would be appreciated. 2 Reply Link to post Share on other sites More sharing options...
deissi Posted February 15, 2010 Report Share Posted February 15, 2010 Help from your side would be appreciated too. Care to share any information you've been given? Thanks . 3 Reply Link to post Share on other sites More sharing options...
ibworking Posted February 15, 2010 Author Report Share Posted February 15, 2010 Well, it's like star numbers which are 1,13,37,73,121,181. I have figured out the patter which is each number adds b multiples of 12. For example, 1+12=13, 13+24=37, 37+36=73 and so on. So it's not arithmetic, geometric or infinite series. 1 Reply Link to post Share on other sites More sharing options...
sweetnsimple786 Posted February 15, 2010 Report Share Posted February 15, 2010 Have you heard of polynomial or quadratic sequences? The way it's been explained to me is you take the terms and find the positive difference between each consecutive term. Then you have a new list of numbers and you find the difference between each terms again, which gives a new list. Then you do the same thing again. You repeat this until you've found a list with all of the same numbers. If you get a list with all of the same numbers, then you know that there's a polynomial that will fit your sequence. So for example 1, d+1, 2d+1, 3d+1[take difference]d, d, dSo that's a first degree polynomial... aka a monomial, which is what you deal with when you say an = a1 + (n-1)d, where d is the difference, because when you simplify, you get an=dn-d+a1More complicated: 1, d+1, 3d+1, 6d+1[take diff]d, 2d, 3d[take diff]d, dSince you've had to take the difference twice, it's a quadratic. If you had to take it thrice, the polynomial would be a cubic. And so on. Does that help you? 6 Reply Link to post Share on other sites More sharing options...
ibworking Posted February 15, 2010 Author Report Share Posted February 15, 2010 I think I get what you mean could you give me an example with numbers though if you have time. Like say hexagonal numbers 1,6,15,28,45..... if you break them down it comes to 5,9,13,17,21 ..... and if you break that down it becomes 4,4,4,4,4. But how would I find a general statment for that? Reply Link to post Share on other sites More sharing options...
sweetnsimple786 Posted February 16, 2010 Report Share Posted February 16, 2010 I'll try to explain this quickly because I elaborate right now, so sorry. So you have the quadratic an2 +bn +c= an[where n is the nth term] Now plug in the known values. You'll have to use three "points" (n, an) like (x,y) because you're solving for a, b, and c. So you'll create a system of equations. Here's a couple of them w/ your hexagonal numbers: n=1, an = 1a + b + c =1n=2, an=64a + 2b + c=6So continue that & solve for a, b, and c, and you'll know how to find an 3 Reply Link to post Share on other sites More sharing options...
saltysummers Posted February 17, 2010 Report Share Posted February 17, 2010 my first math portfolio is due in three days. we were given the one about the stellar numbers. I am about halfway through, but i am stuck on finding a formula for the stellar numbers. for the 6-stellar number, i found the pattern is you add the previous multiple of 12 to the previous stellar number. but how do you put this in an equation?example:table:1 12 133 37to find 37, you go 2(12)+ 13. Reply Link to post Share on other sites More sharing options...
IBJunior2011 Posted February 20, 2010 Report Share Posted February 20, 2010 (edited) I need help on this too. What does the part "Hence, produce a general statement, in terms of p and n, that generates the sequence of p-stellar numbers for any value of p at Snmy first math portfolio is due in three days. we were given the one about the stellar numbers. I am about halfway through, but i am stuck on finding a formula for the stellar numbers. for the 6-stellar number, i found the pattern is you add the previous multiple of 12 to the previous stellar number. but how do you put this in an equation?example:table:1 12 133 37to find 37, you go 2(12)+ 13.The formula I got was ------- Edited February 20, 2010 by sweetnsimple786 We're here to help each other through math IAs by showing how to do something, not giving answers. Please help by explaining but not doing the work for someone. Also, you can use the 'Edit' button to add something to the last post. 2 Reply Link to post Share on other sites More sharing options...
ibworking Posted February 22, 2010 Author Report Share Posted February 22, 2010 What does it mean by assigning different p values? Does it mean different star numbers? And if so could a five star numbers be generate like 1,11,31... and so on. Just wanted to know if I was on the right track. Reply Link to post Share on other sites More sharing options...
scubasteve987 Posted February 23, 2010 Report Share Posted February 23, 2010 What does it mean when it says, "Discuss the scope or limitations of the general statement"? Reply Link to post Share on other sites More sharing options...
sweetnsimple786 Posted February 24, 2010 Report Share Posted February 24, 2010 What does it mean by assigning different p values? Does it mean different star numbers? And if so could a five star numbers be generate like 1,11,31... and so on. Just wanted to know if I was on the right track.I can try to interpret if you write the instructions out, maybe. What does it mean when it says, "Discuss the scope or limitations of the general statement"?Generally, that means what does the statement account for and what does it not? When does it not work? You usually want to look at domain and range and maybe there's something special about your equation that needs to be explained for when it can be used. 1 Reply Link to post Share on other sites More sharing options...
Mark.Begun Posted March 1, 2010 Report Share Posted March 1, 2010 I have started the assesment and am doing well, but I need help with finding the formula that links the numbers 1, 13, 37, 73, 121, 181. I know that there is an increase of a multiple of 12 each time, but the sequence is not arithemetic, geometric OR infinite. We have not learned sequences outside of this area. If someone can help, even by just telling me what PART of sequences this comes from, I will be very appreciative. Reply Link to post Share on other sites More sharing options...
surviveib Posted March 3, 2010 Report Share Posted March 3, 2010 (edited) Here, I have attached the Math Portfolio.Any help would be appreciated, hopefully it will help explaining the question better. Edited March 3, 2010 by surviveib Reply Link to post Share on other sites More sharing options...
sweetnsimple786 Posted March 4, 2010 Report Share Posted March 4, 2010 ...I don't think you asked a question about the directions. Is your question What does it mean by assigning different p values? Does it mean different star numbers? And if so could a five star numbers be generate like 1,11,31... and so on. Just wanted to know if I was on the right track.The directions say p is the number of vertices on the star. That's not the same thing as the star/stellar number, which is the number of dots on the diagram, if I'm interpreting correctly. Make sense? Reply Link to post Share on other sites More sharing options...
Dot. Posted March 7, 2010 Report Share Posted March 7, 2010 Hello fellow past present and future IBers,I'm new to this concept of having to write a Maths Portfolio/IA, and I was wondering if anyone had some helpful tips, some do's and don't's. Also, it would be much appreciated if someone could help explain how my work and writing should be formatted, and if I should explain the concepts I used to come to my answers in-depth.If you or anyone you know could help myself and the few people I write for, it would be greatly appreciated.Many thanks,Dot.PS: If it is of any concern, the Portfolio I'm writing is Type I: Investigating Stellar Numbers; if needed, I can attach a scanned copy of the assignment. Reply Link to post Share on other sites More sharing options...
sweetnsimple786 Posted March 7, 2010 Report Share Posted March 7, 2010 Hey. I merged your topic with this already existing one. For format, look at the links on this thread: http://www.ibsurvival.com/topic/5565-mathematics-forum-rules-the-ia/To answer some questions, yes explain thoroughly. You're supposed to be able to do the IA in about 2-4 hours, but it normally take people much longer. Usually the math is much faster than the writing up process. And what do you mean "If you could help myself and the few people I write for, it would be greatly appreciated." Just wondering. =)You can also find useful things on Google like this document: http://www.cic-caracas.org/vanas/vanascontent/handouts/davis2.pdf Reply Link to post Share on other sites More sharing options...
Dot. Posted March 7, 2010 Report Share Posted March 7, 2010 (edited) Hey. I merged your topic with this already existing one. For format, look at the links on this thread: http://www.ibsurvival.com/topic/5565-mathematics-forum-rules-the-ia/To answer some questions, yes explain thoroughly. You're supposed to be able to do the IA in about 2-4 hours, but it normally take people much longer. Usually the math is much faster than the writing up process. And what do you mean "If you could help myself and the few people I write for, it would be greatly appreciated." Just wondering. =)You can also find useful things on Google like this document: http://www.cic-caracas.org/vanas/vanascontent/handouts/davis2.pdf 'Twas supposed to read 'And a few other people I write for'; simple error, my bad.Also, thanks for moving my post into the correct area! Edited March 7, 2010 by Dot. Reply Link to post Share on other sites More sharing options...
swim625qt Posted March 8, 2010 Report Share Posted March 8, 2010 (edited) Ok so for the first part I got this:n __ #1 __ 1 ---> 1-3= 2 ---> 2-3=12 __ 3 ---> 3-6= 3 ---> 3-4=13 __ 6 ---> 6-10=4 ---> 4-5=14 __ 10 ---> 10-15=55 __ 15But how does this help me arrive at a equation?For the second part:I understand that for U2=12 (2) + 13 and U3= 12 (3) + 37. But how do i turn this into an equation?Any help would be greatly appreciated. Thanks Edited March 8, 2010 by swim625qt Reply Link to post Share on other sites More sharing options...
Popular Post sweetnsimple786 Posted March 8, 2010 Popular Post Report Share Posted March 8, 2010 Ok so for the first part I got this:n __ #1 __ 1 ---> 1-3= 2 ---> 2-3=12 __ 3 ---> 3-6= 3 ---> 3-4=13 __ 6 ---> 6-10=4 ---> 4-5=14 __ 10 ---> 10-15=55 __ 15But how does this help me arrive at a equation?For the second part:I understand that for U2=12 (2) + 13 and U3= 12 (3) + 37. But how do i turn this into an equation?Any help would be greatly appreciated. ThanksI think the method is called finite differences, so you may want to Google that. I'll try to outline it below using different numbers. Have you heard of polynomial or quadratic sequences? The way it's been explained to me is you take the terms and find the positive difference between each consecutive term. Then you have a new list of numbers and you find the difference between each terms again, which gives a new list. Then you do the same thing again. You repeat this until you've found a list with all of the same numbers. If you get a list with all of the same numbers, then you know that there's a polynomial that will fit your sequence. So for example 1, d+1, 2d+1, 3d+1[take difference]d, d, dSo that's a first degree polynomial... aka a monomial, which is what you deal with when you say an = a1 + (n-1)d, where d is the difference, because when you simplify, you get an=dn-d+a1More complicated: 1, d+1, 3d+1, 6d+1[take diff]d, 2d, 3d[take diff]d, dSince you've had to take the difference twice, it's a quadratic. If you had to take it thrice, the polynomial would be a cubic. And so on. Does that help you? I think I get what you mean could you give me an example with numbers though if you have time. Like say hexagonal numbers 1,6,15,28,45..... if you break them down it comes to 5,9,13,17,21 ..... and if you break that down it becomes 4,4,4,4,4. But how would I find a general statment for that?So you're looking for a quadratic for reasons mentioned above in this post. The general form of a quadratic will be an2 +bn +c= an[where n is the nth term] Now plug in the known values. You'll have to use three "points" (n, an) like (x,y) because you're solving for a, b, and c. So you'll create a system of equations. Here's a couple of them w/ your hexagonal numbers: n=1, an = 1a + b + c =1n=2, an=64a + 2b + c=6"You can also use the point (3, 15)9a + 3b + c = 15Now you're just solving for a, b, and c using a system of equations. 4a+2b+c=6- a+ b+ c=1-----------------3a+b=5Now try to get another equation with no c in it. 9a+3b+c=15-(4a+2b+c=6)---------------5a+b=9so 3a+b=55a+b=9Subtract one equation from the other and you get2a=4a=2Now plug in your a value to find b. 5a+b=95(2)+b=9b=-1Now plug in a and b to find ca+b+c=12-1+c=1c=0so the equation would be 2n2 - n = anDoes that help you? 14 Reply Link to post Share on other sites More sharing options...
AV93 Posted March 10, 2010 Report Share Posted March 10, 2010 (edited) Hey, i just got the stellar number portfolio and sheet and i am really lost on how to do it, infact, even how to start it. Any suggestions and tips would be helpful. If any of you could upload or email me yours that would be greatly appreciated. Don't worry i won't plagiarize or copy any. Thank you:)Help from your side would be appreciated too. Care to share any information you've been given? Thanks .You got 42 points? Edited March 10, 2010 by sweetnsimple786 Please use the "Edit" button to add things to a post rather than double posting. Reply Link to post Share on other sites More sharing options...
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